Multiplicatio...

Multiplication of a Vector by a Scalar

Trending Questions

Q. If

\to a =^i + 2^j + 2^k

and

\to b = 3^i + 6^j + 2^k

, then the vector in the direction of

\to a

and having magnitude as

| \to b |

, is

$7 (^i + 2^j + 2^k)$
$\frac{7}{9} (^i + 2^j + 2^k)$
$\frac{7}{3} (^i + 2^j + 2^k)$
$N o n e o f t h e s e$

View Solution

Which of the following is true about multiplication of a vector by a scalar.

1) Scalar multiplication by a positive number other than 1 changes its magnitude but not direction.

2) Scalar multiplication always lead to change in magnitude and direction.

3) Scalar multiplication by -1 will not change the magnitude of the vector but will change its direction.

4) Scalar multiplication by a negative number other than -1 will reverse its direction and change its magnitude as well.

All are correct
1 and 4 are correct
2, 3 and 4 are correct
1, 3 and 4 are correct

View Solution

Q. Find the sum of the vectors

\to a =^i - 2^j +^k, \to b = - 2^i + 4^j + 5^k

and

\to c =^i - 6^j - 7^k

View Solution

Q. If

\to a, \to b, \to c

are position vectors of the vertices of a triangle

A B C

respectively, then length of the perpendicular drawn from

C

A B

$\frac{∣ ∣ ∣ \to a \times \to b + \to b \times \to c + \to c \times \to a ∣ ∣ ∣}{| \to a - \to b |}$
$\frac{∣ ∣ ∣ \to a \times \to b + \to b \times \to c + \to c \times \to a ∣ ∣ ∣}{| \to b - \to c |}$
$\frac{∣ ∣ ∣ \to a \times \to b + \to b \times \to c + \to c \times \to a ∣ ∣ ∣}{| \to a - \to c |}$
$∣ ∣ ∣ \to a \times \to b + \to b \times \to c + \to c \times \to a ∣ ∣ ∣$

View Solution

Q. In a triangle

A B C,

points

D, E

and

F

are taken on the sides

B C, C A

and

A B

respectively, such that

\frac{B D}{D C} = \frac{C E}{E A} = \frac{A F}{F B} = n .

Then Area of

△ D E F

is equal to

$\frac{n^{2} - n + 1}{2 (n + 1)^{2}} \cdot Area (△ A B C)$
$\frac{n^{2} - n + 1}{(n + 1)^{2}} \cdot Area (△ A B C)$
$\frac{n^{2} + n + 1}{2 (n - 1)^{2}} \cdot Area (△ A B C)$
$\frac{n^{2} + n + 1}{(n - 1)^{2}} \cdot Area (△ A B C)$

View Solution

Q. For any four points

P, Q, R, S,

| - - \to P Q \times - - \to R S - - - \to Q R \times - \to P S + - - \to R P \times - - \to Q S |

is equal to

4

times the area of the triangle

$P Q R$
$Q R S$
$P R S$
$P Q S$

View Solution

Q. If the position vectors of A, B, C, D are

\to a, \to b . 2 \to a + 3 \to b, \to a - 2 \to b

respectively, then

\to A C, \to D B, \to B A, \to D A

are?

$\to a + 3 \to b, 3 \to b - \to a, \to a - \to b, 2 \to b$
$2 \to b, \to b - 2 \to a, 3 \to b + \to a, \to b - \to a$
$\to a - 3 \to b, 3 \to b - \to a, \to a + \to b, 2 \to b$
$- 2 \to b, \to b - 2 \to a, 3 \to b - \to a, \to b - \to a$

View Solution

a ≥ 0
a > 0
a ≤ 0
a < 0

View Solution

[\to a + 2 \to b - \to c, \to a - \to b, \to a - \to b - \to c] =

$2 [\to a, \to b, \to c]$
$0$
$3 [\to a, \to b, \to c]$
$[\to a, \to b, \to c]$

View Solution

Q. If p = (3, 5), then 2p, -4p and

\frac{1}{3}

p are respectively (a, b), (c, d) and (e, 5/3). Find the value of -(a+b+c+d+e)

View Solution

Q. If

2 \to a + 3 \to b + 4 \to c = 0 \Rightarrow \to a \times \to b + \to b \times \to c + \to c \times \to a =

$0$
$3 \to a \times \to b$
$3 \to b \times \to c$
$3 \to c \times \to a$

View Solution

Q. Let

A, B, C, D

are any four points in space. If

∣ ∣ ∣ - - \to A B \times - - \to C D + - - \to B C \times - - \to A D + - - \to C A \times - - \to B D ∣ ∣ ∣ = λ \times

(Area of

△ A B C

), then the value of

λ

is:

View Solution

Q. If

a^{b} = b^{c} = a b

, then

b + c

always equals?

$\frac{1}{2} b c$
$b c$
$\frac{1}{b c}$
$1$

View Solution

Q. If

¯ a, ¯ b, ¯ c

are unit vectors such that

¯ a + ¯ b + ¯ c = ¯ 0

, then

¯ a . ¯ b + ¯ b . ¯ c + ¯ c . ¯ a =

$\frac{3}{2}$
$- \frac{3}{2}$
$\frac{1}{2}$
$- \frac{1}{2}$

View Solution

Which of the following is true about multiplication of a vector by a scalar.

1) Scalar multiplication by a positive number other than 1 changes its magnitude but not direction.

2) Scalar multiplication always lead to change in magnitude and direction.

3) Scalar multiplication by -1 will not change the magnitude of the vector but will change its direction.

4) Scalar multiplication by a negative number other than -1 will reverse its direction and change its magnitude as well.

All are correct
1 and 4 are correct
1, 3 and 4 are correct
2, 3 and 4 are correct

View Solution

Q. If

\to a =^i +^j + 2^k

and

\to b = 3^i + 2^j -^k

, find the value of

(\to a + 3 \to b) . (2 \to a - \to b)

View Solution

Q. If

\to a =^i + 2^j + 2^k

and

\to b = 3^i + 6^j + 2^k

, then the vector in the direction of

\to a

and having magnitude as

| \to b |

, is

$N o n e o f t h e s e$
$7 (^i + 2^j + 2^k)$
$\frac{7}{9} (^i + 2^j + 2^k)$
$\frac{7}{3} (^i + 2^j + 2^k)$

View Solution

Q. Which of the following is true about multiplication of a vector by a scalar.

1) Scalar multiplication by a positive number other than 1 changes its magnitude but not direction.

2) Scalar multiplication always lead to change in magnitude and direction.

3) Scalar multiplication by -1 will not change the magnitude of the vector but will change its direction.

4) Scalar multiplication by a negative number other than -1 will reverse its direction and change its magnitude as well.

2, 3 and 4 are correct
1, 3 and 4 are correct
1 and 4 are correct
All are correct

View Solution

Q. Let

\to a = -^i -^k, \to b = -^i +^j and \to c =^i + 2^j + 3^k

be three given vectors. If

\to r

is a vector such that

\to r \times \to b = \to c \times \to b and \to r . \to a = 0,

then the value of

\to r . \to b

View Solution

Q. If

\to a =^i + 2^j + 2^k

and

\to b = 3^i + 6^j + 2^k

, then the vector in the direction of

\to a

and having magnitude as

| \to b |

, is

$7 (^i + 2^j + 2^k)$
$\frac{7}{9} (^i + 2^j + 2^k)$
$\frac{7}{3} (^i + 2^j + 2^k)$
$N o n e o f t h e s e$

View Solution

Q. Classify the following as scalar and vector quantities.
(i) Time period
(ii) Distance
(iii) Force
(iv) Velocity
(v) Work done

View Solution

Q. Unit vector perpendicular to the plane of the triangle

A B C

with position vectors of the vertices

A, B, C,

(

where

Δ

is the area of the triangle

A B C

) .

$\frac{(\to a \times \to b + \to b \times \to c + \to c \times \to a)}{Δ}$
$\frac{(\to a \times \to b + ¯ ¯ b \times \to c + \to c \times \to a)}{2 Δ}$
$\frac{(\to a \times \to b + \to b \times \to c + \to c \times \to a)}{3 Δ}$
$\frac{(\to a \times \to b + \to b \times \to c + \to c \times \to a)}{4 Δ}$

View Solution

Q. Prove that

\to (a \to b) \times (\to c \to d) = [\to (a \to b \to d] \to [a \to b \to c] \to d

View Solution

Q. If p = (3, 5), then 2p, -4p and

\frac{1}{3}

p are respectively (a, b), (c, d) and (e, 5/3). Find the value of -(a+b+c+d+e)

View Solution

Q. If

[\to a \to b \to c] = 2

, then find the value of

[(\to a + 2 \to b - \to c (\to a - \to b) (\to a - \to b - \to c)]

$6$
$8$
$12$
$11$

View Solution

Q. If p = (3, 5), then 2p, -4p and

\frac{1}{3}

p are respectively (a, b), (c, d) and (e, 5/3). Find the value of -(a+b+c+d+e)

View Solution

Q. The values of

λ

such than

(x, y, z) \neq (0, 0, 0)

and

(^i +^j + 3^k) x + (3^i - 3^j +^k) y + (- 4^i + 5^j) z = λ (x^i + y^j + z^k)

are

View Solution